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We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
In the problem of 2-coloring without monochromatic triangles (or triangle-tree 2-coloring), vertices of the simple, connected, undirected graph are colored with either 'black' or 'white' such that there are no 3 mutually adjacent vertices…
We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which…
Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent…
Unrooted phylogenetic networks are graphs used to represent evolutionary relationships. Accurately reconstructing such networks is of great relevance for evolutionary biology. It has recently been conjectured that all phylogenetic networks…
The Maximum Agreement Forest (Maf) problem is a well-studied problem in evolutionary biology, which asks for a largest common subforest of a given collection of phylogenetic trees with identical leaf label-set. However, the previous work…
When using graph transformation rules to implement graph algorithms, a challenge is to match the efficiency of programs in conventional languages. To help overcome that challenge, the graph programming language GP 2 features rooted rules…
In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…
A recurring theme in the least squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least squares estimates of edge lengths. These formulas have proved useful for the development of efficient…
Orthology and paralogy relations are often inferred by methods based on gene similarity, which usually yield a graph depicting the relationships between gene pairs. Such relation graphs are known to frequently contain errors, as they cannot…
A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree.…
The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…
A matching of a graph is a subset of edges no two of which share a common vertex, and a maximum matching is a matching of maximum cardinality. In a $b$-matching every vertex $v$ has an associated bound $b_v$, and a maximum $b$-matching is a…
Here we show that deciding whether two rooted binary phylogenetic trees on the same set of taxa permit a cherry-picking sequence, a special type of elimination order on the taxa, is NP-complete. This improves on an earlier result which…
Orthologous genes, which arise through speciation, play a key role in comparative genomics and functional inference. In particular, graph-based methods allow for the inference of orthology estimates without prior knowledge of the underlying…
The sorting problem is one of the most relevant problems in computer science. Within the scope of modern computer science it has been studied for more than 70 years. In spite of these facts, new sorting algorithms have been developed in…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
An elimination tree for a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root $x$ and recursing on the connected components of $G-x$ to produce the subtrees of $x$. Elimination trees appear in many guises…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…